In an astonishing way, it is relatively easy to introduce uncertainty at the boundary in LAM for ensemble methods, by considering a forcing from an ensemble of global forecast even if the consistency across multiple domains is difficult to handle [1]}; while at a theoretical level, the Kalman forecast equation, in its matrix algebra, is less appropriate to introduce such an uncertainty at boundaries. Note that the difficulty to control the error at the boundary also exists for variational data assimilation [2]}.
